New York City’s 24,000 restaurants — from its internationally known eateries on down to its most modest pizza counters — will have to display large letter grades near their entrances indicating how clean they are under a system approved Tuesday.

The best will get an A, according to the system approved by the city Board of Health.

Officials say the grading system is designed to give potential customers instant access to information about where they are about to eat.

“The grade in the window will give you a sense of how clean the kitchen is, and it will give every restaurant operator an incentive to maintain safe, sanitary conditions,” Health Commissioner Thomas Farley said in a statement.

Some other cities use similar rating systems. Los Angeles grades its restaurants with A for scores of 90 to 100 percent, B for 80 to 89 percent and C for 70 to 79 percent. A restaurant that scores under 70 percent twice in a year is subject to closure.

The New York State Restaurant Association has called the system gimmicky and unfair.

But New York officials say that after Los Angeles began its letter grading system for restaurants, the proportion of restaurants that met the highest standards rose from 40 percent to more than 80 percent.

The details of New York’s system are still being finalized, but the proposal called for grades A through C, based on demerit points accumulated by violations.

Mayor Michael Bloomberg said he’d prefer to eat at a restaurant with an A.

“I think you’re going to find that most restaurants will get to the A status, which is the idea,” he said.

The health department says that most of the restaurants it inspects each year maintain good or excellent health conditions, but that about a quarter of them have “significant lapses in food-safety practices.”

Officials say that about 30 percent of the city’s restaurants would qualify for an A, 40 percent a B and 26 percent a C.

New York City’s restaurant inspection reports are already posted online, but officials said posting the information in restaurant doors and windows prevents diners from having to search for it.

The plan approved Tuesday — after a public hearing and monthlong open comment period — gives restaurants that receive grades lower than an A time to improve their sanitary conditions before they have to post anything.

For those eateries, the health department will return within a month to conduct a second inspection, and the second grade will be posted unless the restaurant operator contests it at the department’s administrative tribunal.

Those restaurants will be allowed to post a sign that says “grade pending” while the matter is being appealed.